相关论文: Grassmann manifold Bosonization of QCD in Two Dime…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
We study the integrability to second order of the infinitesimal Einstein deformations of the symmetric metric $g$ on the complex Grassmannian of $k$-planes inside $\mathbb{C}^n$. By showing the nonvanishing of Koiso's obstruction…
We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in…
We investigate the four-dimensional Wess-Zumino-Witten (WZW) terms within the framework of $Sp$ quantum chromodynamics (QCD) using invertible field theory through bordism theory. We present a novel approach aimed at circumventing both…
We discuss recent results on bosonization in $d \geq 2$ space-time dimensions by giving a very simple derivation for the bosonic representation of the original free fermionic model both in the abelian and non-abelian cases. We carefully…
For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group…
A nonlocal and nonlinear theory of hadrons, equivalent to the color singlet sector two dimensional QCD, is constructed. The phase space space of this theory is an infinite dimensional Grassmannian. The baryon number of QCD corresponds to a…
An effective quantum field theory of the 2D Hubbard model on a square lattice near half-filling is presented and studied. This effective model describes so-called nodal and antinodal fermions, and it is derived from the lattice model using…
The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly…
Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn,…
Non-trivial outer algebra automorphisms may be utilized in $\lambda$-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT…
We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N+1) gauge group. In this theory,…
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The fermion operators are explicitly constructed in terms of the vector potential and the electric field. We carefully…
We extend the bosonization of $2+1$ - dimensional QED with one fermionic flavor performed previously to the case of QED with an induced Chern - Simons term. The coefficient of this term is quantized: $e^2n/8\pi$, $n\in {\bf Z}$. The fermion…
We study the phase diagram of $SU(N)$ gauge theory in three space-time dimensions with a Chern-Simons term at level $k$, coupled to two sets of fundamental fermions with masses $m_1$ and $m_2$, respectively. The two-dimensional phase…
We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $\Sigma_g\times\RrR$ with $\Sigma_g$ a…
Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the…
We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on K\"ahler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to…
I show that physical quantities in several two-dimensional condensed-matter models are related to the Seiberg-Witten calculation of exact quantities in supersymmetric gauge theory. In particular, the magnetization in the Kondo problem and…
In this paper we construct the exact representation of the Ising partition function in the form of the $ SL_q(2,R)$-invariant functional integral for the lattice free $(l,q)$-fermion field theory ($l=q=-1$). It is shown that the…